I think it depends on the player. Hingis is a very intuitive and clever player on court, and she's been playing since her little childhood, so I believe she can manage herself! Tati has no coach and she's not plunging in the rankings!

But some players really need a coach: Mary's attempt to go on with no coach at San Diego and USOpen failed and she explained herself that she was the kind of player who needed a coach, to push do stuff and advise her.